A triomino is a flat L shape made from three square tiles.
A board is divided into squares the same size as the tiles. The board is \(2^n\) by \(2^n\) squares.
One square, anywhere on the board, is coloured blue.
We can put triominoes on the board, but they must not overlap and must not cover the blue square.
Is it possible to cover the board (apart from the blue square) with triominoes? Does it depend on where the blue square is, or on the \(n\) that determines the size of the board? Justify your answer.
Rather than starting with the general \(2^n\) by \(2^n\) board, we could start with some specific values of \(n\).
If we colour one square of a \(2\) by \(2\) board, can we cover the rest with triominoes?
If we colour one square of a \(4\) by \(4\) board, can we cover the rest with triominoes?
And so on…